Assuming you’re the author (and again this is a nice idea!) there is a paper you should check out.

This paper:

https://www.aeaweb.org/articles?id=10.1257/aer.20170116

Is the best case scenario (=easiest) for the exercise you want to do and will illustrate what is hard about the grocery case. In the paper there is:

- One product

- one clearly isolated market.

- four or five firms.

- A clear mechanism for collusion (a government price sharing website).

Even then there is no statistical or econometric test out of the box which “shows collusion”. It’s a great paper (both in my opinion and that’s why it got into AER) but there is nothing they do that says “hey here’s collusion based on this t-stat.”

The grocery case (overlapping markets, thousands of products, many firms) is vastly, vastly harder.

In retail (or any market with elastic pricing, not sure if I'm using that term correctly), collusion is really hard to gain hard evidence (evidence that will hold up in court) using data alone. You need to use the data as a tool for on-the-ground and in-depth qualitative analysis. I would not be surprised if this holds "even more true" for consumer goods like this than it does for other, highly regulated fields like finance and healthcare. I personally like the idea of focusing on an individual good or category of item, and seeing if you can find similar patterns, in other goods.

Actually I’m going to add to your reading list:

“ A Study of Cartel Stability: The Joint Executive Committee, 1880-1886” By Rob Porter (northwestern)

That paper is a classic and I hope porter gets the Nobel prize for the work he has done.

In that paper, we actually know for sure that there was collusion. Porter is trying to assess how hard it was to sustain collusion using the data. (One thing you are not crediting in your website is that collusion is hard to sustain bc all of the colluders have the incentive to cheat!) It takes a lot of assumptions and serious econometric chops to make the analysis credible.

That paper is 40 years old but what you’re really trying to do with your project is called “structural industrial organization.” It’s been around in the economics literature for a long time. It’s my field. It’s hard.

If you want a recent overview which still won’t answer the question the way you wanted to, get “the handbook of industrial organization” edited by hortacsu et al, or the book draft “empirical methods in industrial organization” by aguirregabiria (who is at U Toronto!) or “quantitative techniques for competition and antitrust” by Davis and Garcés.

Good luck.